Masaru Kono$^{a}$ and Paul H. Roberts $^{b}$
$^{a}$ Institute for Study of the Earth's Interior, Okayama University, Misasa, Tottori-ken, Japan. $^{b}$ Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA, USA.
The three-dimensional, fully nonlinear dynamo models first appeared in 1995. A tremendous amount of progress has been achieved since then in the study of the generation mechanism of the Earth's magnetic field. We have recently made a complihensive review of the current status of dynamo simulation and their relevance to the characterization of the observed geomagnetic field behaviors (Kono and Roberts, {\it Reviews of Geophysics}, in press, 2002). In this paper, we will discuss about the possibilities opened up by these numerical simulations for understanding the long term behavior of the geomagnetic field. Among various features, we will place our emphasis on (1) drift of the field in the longitudinal direction, (2) magnetic power spectrum as seen at the surface of the Earth and on the core-mantle boundary (CMB), (3) importance of some low-degree harmonics, and (4) feasibility of statistical model of the magnetic field (such as the giant Gaussian model). The first point is well known for the recent magnetic field from the observations of the westward drift, which has typical duration time of $10^3$ years. However, if we go to longer time scales ($10^4-10^5$ years), it is not clear if the dominant direction of drift is westward or eastward. The exponential decay of the magnetic field power is also well established since the Magsat observation of the global field. This feature seems to be built-in in most of the dynamo models as well. The problems are: what is the decay rate (with the degree of the harmonics) at the CMB, and does the dipole (or quadrupole) term belong to this trend or not? The third one may be more related to the boundary conditions at the CMB than on the dynamo process itself. But some model is found to show a larger fluctuation in the (2,1) harmonics ($g_2^1, h_2^1$) than others, which is rather similar to paleomagnetic observations. The present report gives only examples of the use of dynamo simulation results for understanding the magnetic field behaviors. Although the parameter range covered by the numerical dynamo models is far from what is appropriate for the real Earth, the reported results already provide means to study particular features of the geomagnetic field which are not satisfactorily understood based only on the available observation data.